Properties of gravity near the Schwarzschild radius

The radius of the observable region of the Universe is of the order of its Schwarzschild radius. Due to the spherical symmetry, this allows to check the properties of the gravitational force in the vicinity of the Schwarzschild radius by comparing the theoretical and observed Hubble diagram at high redshifts. This can be done in a simple model that fellows from projective-invariant equations of gravitation.This paper shows that the Hubble diagram up to $z=8$ testifies in favor of the specific properties of gravity near and inside of the Schwarzschild radius.